The Utah Transportation Center (UTC) as well as the Mountain Plains Consortium, sponsored a study to investigate the long-term performance of a deck bulb tee girder bridge. The bridge in question is located in Nibley, Utah and was erected in early 2016. Temperature and prestress losses were analyzed from embedded instrumentation placed within two of the bridge girders before casting. These two girders contained a total of 50 thermocouples and 16 vibrating wire strain gauges. These instruments were placed at the mid-span and end of an exterior girder and the mid-span, quarter-span, and end of a center girder in order to effectively monitor the bridge response in one quarter of the bridge superstructure. The monitoring performed with the thermocouples included the temperature of the girders during curing, weekly maximum and minimum temperatures compared to methods for predicting the average bridge temperature, maximum and minimum thermal gradients at each of the five selected cross sections compared to Code thermal gradients, and thermal camber by measured temperature compared to models to predict thermal gradients. The 16 strain gauges measured prestress losses at four girder cross-sections, which were compared to two predictive methods provided by AASHTO as well as a method by PCI. An additional comparison of the equations provided by AASHTO and a newly available equation used for determining the modulus of elasticity of concretes with a compressive strength of 6,000 – 12,000 psi was performed. Additional exterior instrumentation were provided by Bridge Diagnostics Inc. (BDI) in order to monitor short-term changes within the bridge. A total of 8 strain gauges were attached to the exterior of the girders with 6 attached at the bottom face of 6 girders and 2 attached at the centroid of 2 girders. These sensors as well as the software and wireless data acquisition provided a method to measure the magnitude and frequency of the ranges of strain experienced by the Nibley Bridge.

The spider communities of four stages of a successional sere leading to and including spruce forests were studied in northern Utah. Four seral stages were recognized. These include: meadows, aspen (Populus tremuloides) stands, subalpine fir (Abies lasiocarpa) forest, and the climax Engelmann spruce (Pica engelmanii) forests. During the snow-free periods of 1976, 1977 and 1978, 15,987 spiders were collected by three methods including: pitfall traps, by beating vegetation, and with sweep-net samples. Additionally, 1600 15-second intervals of behavioral observations, and measurements of 182 web locations were made. Of 99 species collected, 44 were considered residents of the sere: criteria for assigning the spiders to foraging strategies (3) and guilds (9) are presented. Five spider communities were ostensively defined--one in the ground stratum of each of the stages and one in the tree stratum of the conifer stages. The data were used to compare the guild strategies of the spiders of the seral stages and to address various hypotheses about successional change in animal community characteristics. Increases with maturity as predicted were observed for 6 spider community parameters including: total biomass, species diversity--richness component, species diversity--equitability component, stratification and spatial heterogeneity, mean organism size, and temporal stratification. A life cycle hypothesis (i.e., short and simple life cycles in early stages, long and complex ones in mature stages) could not be tested because, depending on the life cycle type considered, I found diametrically opposed trends (semi-annual and biennial life cycle types both increased with maturity). The spider species of the ground-stratum meadow community were primarily dispersed in a time dimension (seasonal); the spiders of the tree-stratum community were primarily distributed in a spatial dimension (microhabitat). Spiders of the forest ground-strata communities were dispersed in spatial and temporal dimensions. No dimension was ascertained to be of fundamental importance. Distributions of ground-dwelling species with different foraging strategies, and the resident species of the ground-stratum communities were correlated canonically to 8 environmental variables. Spider species of the meadow community were correlated with a bare dirt variable. Spiders of the aspen community were correlated with 2 environmental variables including: grasses and forbs and a low foliage index. Hunting spiders were correlated with the meadow and aspen variables. Ambushing spiders, web-building spiders, and the spider species of the ground stratum spruce community were correlated with 5 environmental variables including: litter depth, canopy cover, tree basal area, dead leaves and needles, and logs.

Toute perturbation dans les systèmes linéaires peut gravement dégrader la performance des méthodes itératives lorsque les directions conjuguées sont constituées. Ce problème peut être partiellement résolu par les méthodes du gradient à retards, qui ne garantissent pas la descente de la fonction quadratique, mais peuvent améliorer la convergence par rapport aux méthodes traditionnelles. Les travaux ultérieurs se sont concentrés sur les méthodes du gradient alternées avec deux ou plusieurs types de pas afin d'interrompre le zigzag. Des papiers récents ont suggéré que la révélation d'information de second ordre avec des pas à retards pourrait réduire de manière asymptotique les espaces de recherche dans des dimensions de plus en plus petites. Ceci a conduit aux méthodes du gradient avec alignement dans lesquelles l'étape essentielle et l'étape auxiliaire sont effectuées en alternance. Des expériences numériques ont démontré leur efficacité. Cette thèse considère d'abord des méthodes du gradient efficaces pour résoudre les systèmes linéaires symétriques définis positifs. Nous commençons par étudier une méthode alternée avec la propriété de terminaison finie à deux dimensions. Ensuite, nous déduisons davantage de propriétés spectrales pour les méthodes du gradient traditionnelles. Ces propriétés nous permettent d’élargir la famille de méthodes du gradient avec alignement et d’établir la convergence de nouvelles méthodes. Nous traitons également les itérations de gradient comme un processus peu coûteux intégré aux méthodes de splitting. En particulier, nous abordons le problème de l’estimation de paramètre et suggérons d’utiliser les méthodes du gradient rapide comme solveurs internes à faible précision. Dans le cas parallèle, nous nous concentrons sur les formulations avec retards pour lesquelles il est possible de réduire les coûts de communication. Nous présentons également de nouvelles propriétés et méthodes pour les itérations de gradient s-dimensionnelles. En résumé, cette thèse s'intéresse aux trois sujets interreliés dans lesquelles les itérations de gradient peuvent être utilisées en tant que solveurs efficaces, qu’outils intégrés pour les méthodes de splitting et que solveurs parallèles pour réduire la communication. Des exemples numériques sont présentés à la fin de chaque sujet pour appuyer nos résultats théoriques. / Any perturbation in linear systems may severely degrade the performance of iterative methods when conjugate directions are constructed. This issue can be partially remedied by lagged gradient methods, which does not guarantee descent in the quadratic function but can improve the convergence compared with traditional gradient methods. Later work focused on alternate gradient methods with two or more steplengths in order to break the zigzag pattern. Recent papers suggested that revealing of second-order information along with lagged steps could reduce asymptotically the search spaces in smaller and smaller dimensions. This led to gradient methods with alignment in which essential and auxiliary steps are conducted alternately. Numerical experiments have demonstrated their effectiveness. This dissertation first considers efficient gradient methods for solving symmetric positive definite linear systems. We begin by studying an alternate method with two-dimensional finite termination property. Then we derive more spectral properties for traditional steplengths. These properties allow us to expand the family of gradient methods with alignment and establish the convergence of new methods. We also treat gradient iterations as an inexpensive process embedded in splitting methods. In particular we address the parameter estimation problem and suggest to use fast gradient methods as low-precision inner solvers. For the parallel case we focus on the lagged formulations for which it is possible to reduce communication costs. We also present some new properties and methods for s-dimensional gradient iterations. To sum up, this dissertation is concerned with three inter-related topics in which gradient iterations can be employed as efficient solvers, as embedded tools for splitting methods and as parallel solvers for reducing communication. Numerical examples are presented at the end of each topic to support our theoretical findings.

No description available.

A new implicit and compact optimization-based method is presented for high order derivative calculation for finite-volume numerical method on unstructured meshes. Highorder approaches to gradient calculation are often based on variants of the Least-Squares (L-S) method, an explicit method that requires a stencil large enough to accommodate the necessary variable information to calculate the derivatives. The new scheme proposed here is applicable for an arbitrary order of accuracy (demonstrated here up to 3rd order), and uses just the first level of face neighbors to compute all derivatives, thus reducing stencil size and avoiding stiffness in the calculation matrix. Preliminary results for a static variable field example and solution of a simple scalar transport (advection) equation show that the proposed method is able to deliver numerical accuracy equivalent to (or better than) the nominal order of accuracy for both 2nd and 3rd order schemes in the presence of a smoothly distributed variable field (i.e., in the absence of discontinuities). This new Optimization-based Gradient REconstruction (herein denoted OGRE) scheme produces, for the simple scalar transport test case, lower error and demands less computational time (for a given level of required precision) for a 3rd order scheme when compared to an equivalent L-S approach on a two-dimensional framework. For three-dimensional simulations, where the L-S scheme fails to obtain convergence without the help of limiters, the new scheme obtains stable convergence and also produces lower error solution when compared to a third order MUSCL scheme. Furthermore, spectral analysis of results from the advection equation shows that the new scheme is better able to accurately resolve high wave number modes, which demonstrates its potential to better solve problems presenting a wide spectrum of wavelengths, for example unsteady turbulent flow simulations.

Many key problems in machine learning and data science are routinely modeled as optimization problems and solved via optimization algorithms. With the increase of the volume of data and the size and complexity of the statistical models used to formulate these often ill-conditioned optimization tasks, there is a need for new efficient algorithms able to cope with these challenges. In this thesis, we deal with each of these sources of difficulty in a different way. To efficiently address the big data issue, we develop new methods which in each iteration examine a small random subset of the training data only. To handle the big model issue, we develop methods which in each iteration update a random subset of the model parameters only. Finally, to deal with ill-conditioned problems, we devise methods that incorporate either higher-order information or Nesterov’s acceleration/momentum. In all cases, randomness is viewed as a powerful algorithmic tool that we tune, both in theory and in experiments, to achieve the best results. Our algorithms have their primary application in training supervised machine learning models via regularized empirical risk minimization, which is the dominant paradigm for training such models. However, due to their generality, our methods can be applied in many other fields, including but not limited to data science, engineering, scientific computing, and statistics.

The progress of high performance computing platforms is dramatic, and most of the simulations carried out on these platforms result in improvements on one level, yet expose shortcomings of current CFD packages. Therefore, hardware-aware design and optimizations are crucial towards exploiting modern computing resources. This thesis proposes optimizations aimed at accelerating numerical simulations, which are illus- trated in OpenFOAM solvers. A hybrid MPI and GPGPU parallel conjugate gradient linear solver has been designed and implemented to solve the sparse linear algebraic kernel that derives from two CFD solver: icoFoam, which is an incompressible flow solver, and laplacianFoam, which solves the Poisson equation, for e.g., thermal dif- fusion. A load-balancing step is applied using heterogeneous decomposition, which decomposes the computations taking into account the performance of each comput- ing device and seeking to minimize communication. In addition, we implemented the recently developed pipeline conjugate gradient as an algorithmic improvement, and parallelized it using MPI, GPGPU, and a hybrid technique. While many questions of ultimately attainable per node performance and multi-node scaling remain, the ex- perimental results show that the hybrid implementation of both solvers significantly outperforms state-of-the-art implementations of a widely used open source package.

No description available.

The need for solving nonlinear optimization problems is pervasive in many fields. Particle swarm optimization, advantageous with the simple underlying implementation logic, and simultaneous perturbation stochastic approximation, which is famous for its saving in the computational power with the gradient-free attribute, are two solutions that deserve attention. Many researchers have exploited their merits in widely challenging applications. However, there is a known fact that both of them suffer from a severe drawback, non- effectively converging to the global best solution, because of the local “traps” spreading on the searching space. In this article, we propose two approaches to remedy this issue by combined their advantages. In the first algorithm, the gradient information helps optimize half of the particles at the initialization stage and then further updates the global best position. If the global best position is located in one of the local optima, the searching surface’s additional gradient estimation can help it jump out. The second algorithm expands the implementation of the gradient information to all the particles in the swarm to obtain the optimized personal best position. Both have to obey the rule created for updating the particle(s); that is, the solution found after employing the gradient information to the particle(s) has to perform more optimally. In this work, the experiments include five cases. The three previous methods with a similar theoretical basis and the two basic algorithms take participants in all five. The experimental results prove that the proposed two algorithms effectively improved the basic algorithms and even outperformed the previously designed three algorithms in some scenarios.

A blackbody optical fiber thermometer consists of an optical fiber whose sensing tip is given a metallic coating. The sensing tip of the fiber forms an isothermal cavity, and the emission from this cavity is approximately equal to the emission from a blackbody. Standard two-color optical fiber thermometry involves measuring the spectral intensity at the end of the fiber at two wavelengths. The temperature at the sensing tip of the fiber can then be inferred using Planck's law and the ratio of the spectral intensities. If, however, the length of the optical fiber is exposed to elevated temperatures, erroneous temperature measurements will occur due to emission by the fiber. This thesis presents a method to account for emission by the fiber and accurately infer the temperature at the tip of the optical fiber. Additionally, an estimate of the temperature profile along the fiber may be obtained. A mathematical relation for radiation transfer down the optical fiber is developed. The radiation exiting the fiber and the temperature profile along the fiber are related to the detector signal by a signal measurement equation. Since the temperature profile cannot be solved for directly using the signal measurement equation, two inverse minimization techniques are developed to find the temperature profile. Simulated temperature profile reconstructions show the techniques produce valid and unique results. Tip temperatures are reconstructed to within 1.0%. Experimental results are also presented. Due to the limitations of the detection system and the optical fiber probe, the uncertainty in the signal measurement equation is high. Also, due to the limitations of the laboratory furnace and the optical detector, the measurement uncertainty is also high. This leads to reconstructions that are not always accurate. Even though the temperature profiles are not completely accurate, the tip-temperatures are reconstructed to within 1%—a significant improvement over the standard two-color technique under the same conditions. Improvements are recommended that will lead to decreased measurement and signal measurement equation uncertainty. This decreased uncertainty will lead to the development of a reliable and accurate temperature measurement device.